Apart from the gravitational interaction, SHDM can be coupled to ordinary matter also through some super-weak coupling, driven by a high energy scale \(\Lambda >\Lambda _I\)  as the Grand Unification Scale (\(\Lambda _{GUT} \simeq 10^{16}\)  GeV). To assure long-lived particles, the interaction SHDM-SM should be suppressed by some power \(n\)  of the high energy scale \(\Lambda \) , with a decay SHMD \(\rightarrow \)  SM characterised by a lifetime \(\tau _X\simeq (M_X \alpha _{X\Theta })^{-1} (\Lambda /M_X)^{2n-8}\) , being \(\alpha _{X\Theta }\)  the reduced coupling constant between SHDM and SM particles (see [1]} and references therein).
